I got into an accident by I'm not on the insurance

I was driving my mom's car and I got into an accident. My name is not on the insurance. Will it be covered? I was on my way to a job interview and I had a collision with an 18-wheeler. Nobody got hurt but the windows of the right side got shattered and the frames are damaged. It would cost around $3000 to fix. The police gave the truck driver and me a warning and nobody is at fault for the accident. So my question is, will the insurance company help us? Should I even tell the insurance company? The insurance is Progressive. And again the insurance on the car is under my mom's name and not mine.

It would depend whether or not you live with your mom. Insurance companies like for anyone who lives with the insured either be added or excluded from the insurance policy. This is because, if you live with someone, the likelihood of sharing vehicles is quite high and insurance companies want to know all risks they are exposed to. If, however, you don't live with the insured (your mom) or don't use the vehicle frequently (less than 12 times a year, for example), it's very likely the damage will be covered. Some insurance policies have a "permissive user" clause built into them for situations like this. I would check with the policy documentation to see if there's any additional information regarding "permissive user." Best of luck.